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Question:

The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.

Solution:

Let ABCD be a quadrilateral in which ∠A:∠B:∠C:∠D=3:5:9:13
Sum of the ratios=3+5+9+13=30
Also ,∠A+∠B+∠C+∠D=360o
Sum of all the angles of quadrilateral is 360o.
∴∠A=3/30 ×360o=36o
∠B=5/30 ×360o=60o
∠C=9/30 ×360o=108o
∠C=13/30 ×360o=156o